The present invention relates to the monitoring of vibration signals from machines with rotating elements. It is well known that rotating elements within machinery may subject the machinery to vibrations at different vectors related to operating frequency, yet most vibration monitors collect data as a composite for all vectors. As such, a single composite vibration vector is measured even though it results from a composite of, for example, 1× operating frequency, 2× operating frequency, and 3× operating frequency vibration vectors. Conventionally, this composite frequency vector is analyzed as such by hand in analyzation methods that are painstakingly slow. While this technique has been useful, it limits the ability of machine users to analyze and predict the true effects of vibration signals in a more refined manner, for example as separate 1×, 2×, and 3× vectors, and therefore represents a limited approach to machine vibration analysis.